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`        Find the locus of midpoint of variable chord of parabola y2 = 4ax such  that tangents make an angle Φ between them.`
7 years ago

147 Points
```										Dear Priyansh
let the mid point is  (h,k)
and let the point where tangent touch the parabola is (at12,2at1)  and (at22,2at2)

so 2h = a(t12 + t22)    and  2k = 2a(t1+t2)   ...................1

from equation 1 find  the value of t1t2 = (k2 -2ha)/2a2
and |t1-t2| = 1/a {k2 - 4ha}1/2
so given tanΦ =  |m1-m2|/(1+m1m2)
where  m1 = 1/t1
m2 =1/t2

so put  these value
tanΦ =2a{k2 -4ha}1/2 / {k2 -2ha}
Please feel free  to post as many doubts on our discussion forum as you can. If you find any  question Difficult to understand - post it here and we will get you the answer and  detailed  solution very  quickly.   We are all  IITians and here to help you in your IIT JEE preparation.  All the best.   Regards, Askiitians  Experts Badiuddin
```
7 years ago
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